Finite Group Databasebeta

← Group #11920724

Character table — Group #11920724

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222446666888812121212121216161616161616161616242424242424242424242424363636363636484848487272
order1244234612126122244361212246612123666612121212124488121212122424242424888866121244
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ311111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511-1-1-1111-1-1-111-11-111-1-11-11-11-11-1-1-11111-1-1i−ii−iii−i−iii−i−i-11ii−i−i11-1-1i−i
χ611-1-1-1111-1-1-111-11-111-1-11-11-11-11-1-1-11111-1-1−ii−ii−i−iii−i−iii-11−i−iii11-1-1−ii
χ711-1-1-1111-1-1-111-11-111-1-1-111-11-11-1-1-11111-1-1i−ii−iii−i−iii−i−i1-1−i−iii-1-111−ii
χ811-1-1-1111-1-1-111-11-111-1-1-111-11-11-1-1-11111-1-1−ii−ii−i−iii−i−iii1-1ii−i−i-1-111i−i
χ92222222222222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1000000000000220000-1-1-1-100
χ102222222222222222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-20000111100
χ1122222-12-1-1-1-1-12222222200-1-1-1-1-12-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1222222-12-1-1-1-1-12222222200-1-1-1-1-12-1-1-12-1-1-1-1-2-2-2-211111111000000000000
χ132222-22-2222-2-2-222-2222200-222-22-2-2-22-2-2-222000000000000000000000000
χ142222-22-2222-2-2-222-2-1-1-1-100-222-2-1111-1111-1-1000000000000000000−i3i3−i3i300
χ152222-22-2222-2-2-222-2-1-1-1-100-222-2-1111-1111-1-1000000000000000000i3−i3i3−i300
χ162222-2-1-2-1-1-111-222-22222001-1-11-1-211-1-211-1-10000−i3i3−i3i3−i3i3−i3i3000000000000
χ172222-2-1-2-1-1-111-222-22222001-1-11-1-211-1-211-1-10000i3−i3i3−i3i3−i3i3−i3000000000000
χ1822-2-222-22-2-22-2-2-22222-2-200-2-22222222-2-2-2-2-2000000000000000000000000
χ1922-2-222-22-2-22-2-2-222-1-11100-2-222-1-1-1-1-111111000000000000000000−i3i3i3−i300
χ2022-2-222-22-2-22-2-2-222-1-11100-2-222-1-1-1-1-111111000000000000000000i3−i3−i3i300
χ2122-2-22-1-2-111-11-2-22222-2-20011-1-1-12-1-1-1-2111100003−3−333−3−33000000000000
χ2222-2-22-1-2-111-11-2-22222-2-20011-1-1-12-1-1-1-211110000−333−3−333−3000000000000
χ2322-2-2-2222-2-2-222-22-2-1-1112-22-22-2-1111-1-1-1-111000000000000-220000-1-11100
χ2422-2-2-2222-2-2-222-22-2-1-111-222-22-2-1111-1-1-1-1110000000000002-2000011-1-100
χ2522-2-2-2-12-1111-12-22-222-2-200-11-11-1-211-12-1-1112i−2i2i−2i−i−iii−i−iii000000000000
χ2622-2-2-2-12-1111-12-22-222-2-200-11-11-1-211-12-1-111−2i2i−2i2iii−i−iii−i−i000000000000
χ27333333333333-1-1-1-1000033-1-1-1-1000000000011-1-11111-1-1-1-1-1-111110000-1-1
χ28333333333333-1-1-1-1000033-1-1-1-10000000000-1-111-1-1-1-11111-1-1-1-1-1-1000011
χ29333333333333-1-1-1-10000-3-3-1-1-1-1000000000011-1-11111-1-1-1-111-1-1-1-1000011
χ30333333333333-1-1-1-10000-3-3-1-1-1-10000000000-1-111-1-1-1-111111111110000-1-1
χ3133-3-3-3333-3-3-33-11-1100003-3-11-110000000000i−i−iiii−i−i−i−iii1-1ii−i−i0000−ii
χ3233-3-3-3333-3-3-33-11-1100003-3-11-110000000000−iii−i−i−iiiii−i−i1-1−i−iii0000i−i
χ3333-3-3-3333-3-3-33-11-110000-33-11-110000000000i−i−iiii−i−i−i−iii-11−i−iii0000i−i
χ3433-3-3-3333-3-3-33-11-110000-33-11-110000000000−iii−i−i−iiiii−i−i-11ii−i−i0000−ii
χ3544444-24-2-2-2-2-24444-2-2-2-200-2-2-2-21-2111-21111000000000000000000000000
χ364444-4-2-4-2-2-222-444-4-2-2-2-2002-2-2212-1-112-1-111000000000000000000000000
χ3744-4-44-2-4-222-22-4-444-2-2220022-2-21-21112-1-1-1-1000000000000000000000000
χ3844-4-4-4-24-2222-24-44-4-2-22200-22-2212-1-11-211-1-1000000000000000000000000
χ394-44i−4i040-44i−4i000000-222i−2i000000-200020002i−2i00000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ404-44i−4i040-44i−4i000000-222i−2i000000-200020002i−2i000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ414-4−4i4i040-4−4i4i000000-22−2i2i000000-20002000−2i2i000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ424-4−4i4i040-4−4i4i000000-22−2i2i000000-20002000−2i2i00000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ4366666-36-3-3-3-3-3-2-2-2-20000001111000000000022-2-2-1-1-1-11111000000000000
χ4466666-36-3-3-3-3-3-2-2-2-200000011110000000000-2-2221111-1-1-1-1000000000000
χ456666-66-6666-6-62-2-220000002-2-220000000000000000000000000000000000
χ466666-6-3-6-3-3-3332-2-22000000-111-100000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ476666-6-3-6-3-3-3332-2-22000000-111-100000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ4866-6-666-66-6-66-622-2-200000022-2-20000000000000000000000000000000000
χ4966-6-66-3-6-333-3322-2-2000000-1-111000000000000003−3−33−333−3000000000000
χ5066-6-66-3-6-333-3322-2-2000000-1-11100000000000000−333−33−3−33000000000000
χ5166-6-6-6-36-3333-3-22-220000001-11-100000000002i−2i−2i2i−i−iiiii−i−i000000000000
χ5266-6-6-6-36-3333-3-22-220000001-11-10000000000−2i2i2i−2iii−i−i−i−iii000000000000
χ538-88i−8i080-88i−8i0000002-2−2i2i0000002000-2000−2i2i000000000000000000000000
χ548-88i−8i0-404−4i4i0000002-2−2i2i000000-103-3103i−3ii−i000000000000000000000000
χ558-88i−8i0-404−4i4i0000002-2−2i2i000000-10-3310−3i3ii−i000000000000000000000000
χ568-88i−8i0-404−4i4i000000-444i−4i0000002000-2000−2i2i000000000000000000000000
χ578-8−8i8i080-8−8i8i0000002-22i−2i0000002000-20002i−2i000000000000000000000000
χ588-8−8i8i0-4044i−4i0000002-22i−2i000000-103-310−3i3i−ii000000000000000000000000
χ598-8−8i8i0-4044i−4i0000002-22i−2i000000-10-33103i−3i−ii000000000000000000000000
χ608-8−8i8i0-4044i−4i000000-44−4i4i0000002000-20002i−2i000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.